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   [
    3,
    85,
    102,
    136,
    154,
    193,
    195
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   [
    51,
    60,
    86,
    156,
    173,
    191,
    194
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   [
    2,
    77,
    87,
    111,
    192,
    195,
    213
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   [
    9,
    28,
    88,
    112,
    159,
    193,
    196
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   [
    10,
    26,
    89,
    136,
    157,
    197,
    201
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   [
    27,
    90,
    100,
    127,
    158,
    198,
    206
   ],
   [
    25,
    57,
    91,
    159,
    199,
    200,
    207
   ],
   [
    33,
    76,
    92,
    128,
    138,
    160,
    200
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   [
    59,
    74,
    93,
    129,
    161,
    201,
    208
   ],
   [
    7,
    94,
    98,
    141,
    176,
    202,
    204
   ],
   [
    38,
    73,
    95,
    131,
    143,
    200,
    203
   ],
   [
    6,
    64,
    96,
    132,
    201,
    204,
    209
   ],
   [
    5,
    41,
    97,
    134,
    146,
    202,
    205
   ],
   [
    40,
    71,
    98,
    172,
    176,
    192,
    206
   ],
   [
    0,
    92,
    99,
    118,
    173,
    207,
    215
   ],
   [
    13,
    21,
    100,
    119,
    174,
    179,
    208
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   [
    11,
    24,
    101,
    122,
    184,
    208,
    209
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   [
    53,
    58,
    102,
    150,
    163,
    185,
    210
   ],
   [
    1,
    83,
    103,
    151,
    186,
    211,
    214
   ],
   [
    12,
    22,
    104,
    153,
    166,
    187,
    212
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   [
    15,
    20,
    105,
    158,
    171,
    212,
    213
   ],
   [
    4,
    43,
    106,
    137,
    196,
    199,
    214
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   [
    8,
    30,
    107,
    178,
    190,
    205,
    215
   ]
  ]
 },
 "distance": {
  "d": 18,
  "X": {
   "value": 18,
   "confidence": "upper_bound",
   "witness": [
    4,
    5,
    24,
    35,
    37,
    39,
    42,
    44,
    70,
    98,
    112,
    122,
    134,
    145,
    164,
    176,
    189,
    196
   ],
   "witness_provenance": {
    "found_by": [
     "@mathysrennela"
    ],
    "date": "2026-10-12",
    "found_at_samples": 2000,
    "survived_samples": 2000,
    "tool": "research/kit/surrogate.lightest_logical",
    "seeds": [
     1019
    ]
   }
  },
  "Z": {
   "value": 18,
   "confidence": "upper_bound",
   "witness": [
    27,
    61,
    71,
    76,
    77,
    81,
    123,
    130,
    138,
    141,
    148,
    157,
    181,
    192,
    200,
    207,
    210,
    215
   ],
   "witness_provenance": {
    "found_by": [
     "@mathysrennela"
    ],
    "date": "2026-10-12",
    "found_at_samples": 2000,
    "survived_samples": 2000,
    "tool": "research/kit/surrogate.lightest_logical",
    "seeds": [
     1020
    ]
   }
  }
 },
 "provenance": {
  "authors": [
   "Lee, Gideon"
  ],
  "construction": "Two-block group-algebra code C(a,b) over C18 x S3 = SmallGroup(108, 24) (order 108), elements numbered as in GAP Elements(SmallGroup(order,id)) with element 0 the identity. n = 2|G| = 216; H_X = [L(a)|R(b)], H_Z = [R(b)^T|L(a)^T]; a = {0, 8, 62, 80}, b = {0, 22, 57} as element indices. Check weight 7. Parameters and blocks taken from the public code database of arXiv:2610.13880v1 (Lee, 'Bicycle Race'), github.com/gideonlsx/bicycle-race.",
  "references": [
   "arXiv:2610.13880"
  ],
  "date": "2026-10-12",
  "notes": "Parameters and construction taken from the public database of arXiv:2610.13880v1. Distance is an upper bound certified by the witnesses attached here. Parameters and blocks taken from the public code database of arXiv:2610.13880v1 (Lee, 'Bicycle Race'), github.com/gideonlsx/bicycle-race @ aed705a, CC BY 4.0; rebuilt here with the repo's own group data. Distance is an upper bound certified by the attached witnesses, not the paper's exact distance.",
  "origin": "baseline",
  "novelty": "known_parameters",
  "model": "Mimo-V2.6-Flash"
 },
 "family": "2bga-nonabelian"
}